The present invention relates generally to decoding techniques for use in communication systems, and more particularly to noncoherent decoding techniques for use in such systems.
In communication over a fading channel in which the fading is unknown but approximately constant over multiple symbol periods, coherent decoding requires explicit learning of the channel. As a result, its overhead may be excessive, particularly in mobile or multiple antenna settings. Differential modulation is traditionally used when the channel changes the symbol phase in an unknown, but consistent or continuously varying way. Standard differential modulation techniques such as differential M-ary phase shift keying (DMPSK) encode the data in the phase difference between two consecutive symbols. Under the assumption that the unknown fading coefficient changes little between two symbols, the difference in phase is preserved and can be used to carry data. Differential modulation allows the use of noncoherent decoding, thereby avoiding the excessive overhead typically associated with coherent decoding.
Unfortunately, the performance of noncoherent differential decoding is generally inferior to that of coherent decoding. For example, in D. Divsalar and M. K. Simon, xe2x80x9cMaximum-likelihood differential detection of uncoded and trellis codes amplitude phase modulation over AWGN and fading channelsxe2x80x94metrics and performance,xe2x80x9d IEEE Trans. on Comm., Vol. 42, No. 1, pp. 76-89, 1994, it is shown that when the number of phases M gets large, DMPSK suffers from a 3 dB performance loss compared to coherent MPSK decoding. A portion of this loss can be recouped by using maximum likelihood (ML) decoding over blocks of multiple symbols, as described in the above-cited D. Divsalar and M. K. Simon reference. However, the computational complexity of the standard ML algorithm for exact noncoherent decoding is exponential in both the rate R=log2 M and the block length T.
In D. Warrier and U. Madhow, xe2x80x9cNoncoherent Communication in Space and Time,xe2x80x9d http://www.ece.ucsb.edu/Faculty/Madhow/Publications/noncoh_itsubmission, there is described an approximate ML decoding algorithm having a complexity which in some circumstances is linear in the block length T. However, in order for this approximate algorithm to provide a constant approximation quality, its complexity needs to grow quadratically in the block length T, i.e. the complexity of the approximate algorithm for the case of constant approximation quality is given by O(T2), where O(xc2x7) denotes xe2x80x9con the order of.xe2x80x9d
A need therefore exists for an improved noncoherent decoding technique which provides improved performance and reduced complexity relative to the conventional techniques described above.
The present invention provides an improved noncoherent decoding technique for exact maximum likelihood (ML) decoding over blocks of multiple symbols. Unlike the conventional standard noncoherent decoder previously described, the complexity of which is exponential in both the rate R and the block length T, a noncoherent decoder configured in accordance with the present invention has a complexity which is independent of the rate R and linear-logarithmic in the block length (O(T log T)).
In accordance with the invention, received symbols are decoded in a communication system using an exact maximum likelihood block noncoherent decoding algorithm. The noncoherent decoding algorithm utilizes a set of test words determined for a given block of symbols based on a corresponding set of crossover angles which specify transitions between the test words. The set of test words in an illustrative embodiment are given by vectors g[t] for 1xe2x89xa6txe2x89xa6T, where t denotes a particular received symbol in a block of T symbols and each of the vectors includes T elements. The first one of the test words maybe a vector g[1] which is selected as an output of a coherent maximum likelihood decoding operation for a case in which a channel fading coefficient has a value of zero. The crossover angle xcex1, for a given received symbol t in a block of T received symbols is computed as a function of the selected first test word and the corresponding received signal component. The set of crossover angles computed using the first test word are arranged in a sorted list, and are used to determine transitions between the test words. An output of a noncoherent decoding operation for a given received symbol t is given by:             g      ^        =                            g                      [                          t              ^                        ]                          ⁢                  xe2x80x83                ⁢        with        ⁢                  xe2x80x83                ⁢                  t          ^                    =              arg        ⁢                  xe2x80x83                ⁢                              max                          1              ≤              t              ≤              T                                ⁢                      ℒ            ⁡                          (                              g                t                            )                                            ,
where (gt) is a likelihood computed for a given one of the test words as a function of a set of recursively computed inner products involving the block of T received symbols.
The noncoherent decoding algorithm may be implemented using a sliding window corresponding to the block length T, such that the decoding algorithm maintains a sorted list of T crossover angles and T inner products computed using the test words. When the sliding window is adjusted by one position, a crossover angle is dropped from the sorted list and a new crossover angle is determined and inserted in the sorted list, and the inner products are then updated based on the current sorted list.
The present invention can be used with a variety of different types of modulation, including but not limited to phase shift keying (PSK) modulation and quadrature amplitude modulation (QAM). In addition, the invention can be implemented in single-antenna or multiple-antenna communication systems.